Can the grease pencil draw on a plane axis in the perspective view?
You Answered your question yourself.

What you need to do is to add a plane and align it to view  (From the adding option),Using local transform orientation,move the plane in he local z axis to the level you want to draw in.

Now all you have to do is to put your 3D cursor into the surface of the plane just by clicking anywhere in the plane with the LMB .

So suppose I have this object and I want to draw on he shades face:



Now add the plane and pt the 3d cursor on it :



And you are ready to paint,Assuming your stroke placement is set to Cursor,you are good.And you can just delete h plane it is no needed.